• Offered by Department of Mathematics
• ANU College ANU Joint Colleges of Science
• Course subject Mathematics
• Areas of interest Mathematics
• Course convener
• Prof Michael Barnsley
• Mode of delivery In Person
• Offered in Second Semester 2014
Fractal Geometry & Applications to Digital Imaging (MATH3062)

This course introduces the basic mathematical techniques of fractal geometry for diverse applications. It will explain how these techniques apply to digital imaging, image compression, special effects,  biological modeling, medical data representation and cryptography. The key ideas are introduced in an intuitive, hands-on manner, although all students are invited to sit in on the HPO option special lectures which will provide rigorous mathematical foundations.

Each student will be expected to select and complete a special project in one of the following areas: (i) 3D printing  of  fractal models ; (ii) fractal image magnification; (iii) fractal compression ; (iv) project chosen by the student with agreement from the lecturer.  There will be one computer lab meeting each week.

Honours pathway option (HPO)

Students doing the HPO option will participate in an additional lecture each week. These may be related to the material in the basic course, but will be focused on exhibiting and understanding the general theory of Iterated Function Systems.

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the basic concepts of fractal geometry; (LO1)

2. Be able to identify practical situations where fractal techniques may be applied; (LO2)

3. Be able to build a fractal application in a practical area such as  digital imaging or biological modeling. (LO3)

4. (HPO only)  Be able to prove basic theorems and solve problems in the area of Iterated Function Systems. (LO4)

## Indicative Assessment

Assessment may be based on:

• Projects (25%; LO 1-3)
• Tutorials and Lab worksheets (25%; LO 1-3)
• 5 Assignments (25%l  LO 1-3)
• Mid-term Exam (25%; LO 1-3)

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

24 lectures and approx. 10 workshops. Plus 12 additional lectures for HPO

## Requisite and Incompatibility

To enrol in this course you must have successfully completed MATH2305 or MATH2405.

## Prescribed Texts

Fractals Everywhere, by Michael F. Barnsley, Third Edition (2012,  Dover).

## Fees

Tuition fees are for the academic year indicated at the top of the page.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Students continuing in their current program of study will have their tuition fees indexed annually from the year in which you commenced your program. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). You can find your student contribution amount for each course at Fees.  Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee Description
1994-2003 \$1650
2014 \$2946
2013 \$2946
2012 \$2946
2011 \$2946
2010 \$2916
2009 \$2916
2008 \$2916
2007 \$2520
2006 \$2520
2005 \$2298
2004 \$1926
International fee paying students
Year Fee
1994-2003 \$3390
2014 \$3762
2013 \$3756
2012 \$3756
2011 \$3756
2010 \$3750
2009 \$3618
2008 \$3618
2007 \$3618
2006 \$3618
2005 \$3450
2004 \$3450
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### Second Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
8651 21 Jul 2014 01 Aug 2014 31 Aug 2014 30 Oct 2014 In Person N/A